Algorithms in Real Algebraic Geometry

Forsideomslag
Springer Science & Business Media, 6. jul. 2006 - 662 sider
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The algorithmic problems of real algebraic geometry such as real root counting, deciding the existence of solutions of systems of polynomial equations and inequalities, finding global maxima or deciding whether two points belong in the same connected component of a semi-algebraic set appear frequently in many areas of science and engineering. In this textbook the main ideas and techniques presented form a coherent and rich body of knowledge.

Mathematicians will find relevant information about the algorithmic aspects. Researchers in computer science and engineering will find the required mathematical background.

Being self-contained the book is accessible to graduate students and even, for invaluable parts of it, to undergraduate students.

This second edition contains several recent results, on discriminants of symmetric matrices, real root isolation, global optimization, quantitative results on semi-algebraic sets and the first single exponential algorithm computing their first Betti number.

 

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Indhold

II
11
III
20
IV
25
V
27
VI
29
VII
44
IX
52
X
57
LXXIV
303
LXXV
307
LXXVI
314
LXXVII
316
LXXVIII
317
LXXIX
322
LXXX
323
LXXXI
326

XI
63
XII
69
XIII
71
XIV
72
XV
74
XVI
81
XVII
83
XVIII
86
XIX
87
XX
93
XXI
94
XXII
99
XXIII
100
XXIV
105
XXV
110
XXVI
113
XXVII
119
XXIX
127
XXX
132
XXXI
136
XXXII
143
XXXIII
149
XXXIV
153
XXXV
157
XXXVI
159
XXXVII
168
XXXVIII
170
XXXIX
172
XL
174
XLI
181
XLII
183
XLIII
186
XLIV
191
XLV
194
XLVI
195
XLVII
199
XLVIII
201
XLIX
206
L
209
LI
213
LII
221
LIII
223
LIV
226
LVI
228
LVII
231
LVIII
234
LIX
236
LX
237
LXI
256
LXII
262
LXIII
268
LXIV
273
LXV
280
LXVI
281
LXVII
292
LXIX
294
LXX
299
LXXI
300
LXXII
301
LXXXII
330
LXXXIII
333
LXXXIV
334
LXXXV
337
LXXXVI
344
LXXXVII
350
LXXXVIII
351
LXXXIX
360
XC
383
XCI
397
XCII
401
XCIII
402
XCIV
404
XCVI
408
XCVII
415
XCVIII
423
XCIX
426
C
428
CI
430
CII
440
CIII
444
CIV
445
CV
451
CVI
456
CVII
462
CVIII
471
CIX
483
CX
495
CXI
498
CXII
503
CXIII
505
CXIV
506
CXV
516
CXVI
519
CXVII
528
CXVIII
532
CXIX
533
CXX
534
CXXI
547
CXXII
551
CXXIII
557
CXXIV
558
CXXV
562
CXXVI
563
CXXVII
564
CXXVIII
568
CXXIX
580
CXXX
592
CXXXI
593
CXXXII
601
CXXXIII
608
CXXXIV
614
CXXXV
617
CXXXVI
627
CXXXVII
633
CXXXVIII
635
CXXXIX
644
CXL
655
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